The present disclosure is directed to a novel use of time reversal in imaging applications.
Locating and imaging targets buried in high clutter poses considerable challenges. Detection and imaging algorithms suffer significant performance loss because the channel Green's function is very different from the direct path model that these algorithms usually assume. In complex channels, for example, when the propagation speed profile is spatially varying or due to boundary layers, the use of numerical codes that integrate the wave equation, like matched field processing (MFP) in underwater acoustics, e.g., [1], provides the channel Green's function. But MFP is prohibitively expensive in most applications and is highly sensitive to accurate knowledge of the environmental conditions.
This disclosure explores how time reversal (TR) can be used in localizing targets in highly cluttered environments. References [2], [3], [4], [5], [6] have shown the power of time reversal to focus with super-resolution on a source in a highly dispersive medium by time reversing and retransmitting the time dispersed signal received at an array of sensors. References [7], [8] demonstrate super-resolution focusing in underwater acoustics and reference [9] demonstrates focusing in the electromagnetic domain. Focusing results from the time reversibility of the wave equation in a non-absorbing medium: The highly dispersed back-propagated field is time reversed (or phase conjugate in the frequency domain), energy normalized, resent, and focuses on the radiating source. The more inhomogeneous the media is, the higher the focusing resolution achieved. Intuitively, time reversal is equivalent to generating a virtual aperture larger than its actual physical size, yielding a much higher resolution. Beyond focusing, recent works on time reversal imaging include Lehman and Devaney [10], Devaney [11], Prada and Thomas [12], Borcea et al. [13], [14], and the references therein. In these works, the Multiple Signal Classification (MUSIC) algorithm is combined with time reversal for locating well resolved targets, where the MUSIC spectrum is constructed by eigen-decomposing the so called time reversal matrix. This approach is applicable only when the number of scatterers in the imaged area is smaller than the number of antennas because the generalized MUSIC spectrum requires that the number of scatterers be smaller than the number of antennas.